An Adaptive Finite Element PML Method for the Open Cavity Scattering Problems

An Adaptive Finite Element Pml Method for the Elastic Wave Scattering Problem in Periodic Structures

ABSTRACT. An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic and rigid surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the perfectly matched layer (PML) technique. The well-posedness and exponential convergence of the solution are established for the truncated PML pro...

An Adaptive Finite Element Method for Nonlinear Optimal Control Problems

An Adaptive Finite Element Method for Linear Elliptic Problems

We propose an adaptive finite element method for linear elliptic problems based on an optimal maximum norm error estimate. The algorithm produces a sequence of successively refined meshes with a final mesh on which a given error tolerance is satisfied. In each step the refinement to be made is determined by locally estimating the size of certain derivatives of the exact solution through compute...

An Adaptive Finite Element Method

We develop an adaptive nite element algorithm for reactive ow simulations. The underlying equations are the Navier-Stokes equations for low-Mach-number ows and an additional system of convection-diiusion-reaction equations for the chemical species. Especially in combustion problems the reaction terms are very stii and nonlinear. This set of equations represents a complicated system of PDEs whic...

An adaptive finite element method for magnetohydrodynamics

We describe a procedure for the adaptive h-refinement solution of the incompressible MHD equations in stream function form using a stabilized finite element formulation. The mesh is adapted based on a posteriori spatial error estimates of the magnetic field using both recovery and order extrapolation techniques. The step size for time integration is chosen so that temporal discretization errors...